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A Priori Estimates for the Homogeneous Monge-Ampère Equation on Kähler Manifolds

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thesis
posted on 2019-10-16, 18:48 authored by Katherine Ann BrubakerKatherine Ann Brubaker
This thesis investigates the existence of smooth solutions to MA(F), proving a priori estimates on the leaves of the foliation that corresponds to smooth solutions. We demonstrate that sequences of leaves of Monge-Amp`ere foliations converge to holomorphic disks.

History

Degree Type

  • Doctor of Philosophy

Department

  • Mathematics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Laszlo Lempert

Additional Committee Member 2

Sai-Kee Yeung

Additional Committee Member 3

Steven R. Bell

Additional Committee Member 4

Chi Li

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    Categories

    Keywords

    complex geometryseveral complex variablesNon-linear partial differential equationsfoliationKahler manifoldsspace of Kahler metricsMonge-Ampere equationPure Mathematics not elsewhere classifiedMathematical Sciences not elsewhere classified

    Licence

    CC BY 4.0

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